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Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process. (English) Zbl 1417.60073

Summary: In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

MSC:

60J65 Brownian motion
60H20 Stochastic integral equations
40D25 Inclusion and equivalence theorems in summability theory
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